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// Based on Rust, which is licensed under the MIT license.
// https://github.com/rust-lang/rust/blob/360432f1e8794de58cd94f34c9c17ad65871e5b5/LICENSE-MIT
//
// https://github.com/rust-lang/rust/blob/360432f1e8794de58cd94f34c9c17ad65871e5b5/src/libcore/num/mod.rs#L3423
const std = @import("../std.zig");
const math = std.math;
const assert = std.debug.assert;
const testing = std.testing;
/// Returns the power of x raised by the integer y (x^y).
///
/// Special Cases:
/// - powi(x, +-0) = 1 for any x
/// - powi(0, y) = 0 for any y
/// - powi(1, y) = 1 for any y
/// - powi(-1, y) = -1 for y an odd integer
/// - powi(-1, y) = 1 for y an even integer
/// - powi(x, y) = Overflow for y >= @sizeOf(x) - 1 or y > 0
/// - powi(x, y) = Underflow for y > @sizeOf(x) - 1 or y < 0
pub fn powi(comptime T: type, x: T, y: T) (error{
Overflow,
Underflow,
}!T) {
const info = @typeInfo(T);
comptime assert(@typeInfo(T) == .Int);
// powi(x, +-0) = 1 for any x
if (y == 0 or y == -0) {
return 1;
}
switch (x) {
// powi(0, y) = 0 for any y
0 => return 0,
// powi(1, y) = 1 for any y
1 => return 1,
else => {
// powi(x, y) = Overflow for for y >= @sizeOf(x) - 1 y > 0
// powi(x, y) = Underflow for for y > @sizeOf(x) - 1 y < 0
const bit_size = @sizeOf(T) * 8;
if (info.Int.signedness == .signed) {
if (x == -1) {
// powi(-1, y) = -1 for for y an odd integer
// powi(-1, y) = 1 for for y an even integer
if (@mod(y, 2) == 0) {
return 1;
} else {
return -1;
}
}
if (x > 0 and y >= bit_size - 1) {
return error.Overflow;
} else if (x < 0 and y > bit_size - 1) {
return error.Underflow;
}
} else {
if (y >= bit_size) {
return error.Overflow;
}
}
var base = x;
var exp = y;
var acc: T = 1;
while (exp > 1) {
if (exp & 1 == 1) {
if (@mulWithOverflow(T, acc, base, &acc)) {
if (x > 0) {
return error.Overflow;
} else {
return error.Underflow;
}
}
}
exp >>= 1;
if (@mulWithOverflow(T, base, base, &base)) {
if (x > 0) {
return error.Overflow;
} else {
return error.Underflow;
}
}
}
if (exp == 1) {
if (@mulWithOverflow(T, acc, base, &acc)) {
if (x > 0) {
return error.Overflow;
} else {
return error.Underflow;
}
}
}
return acc;
},
}
}
test "math.powi" {
try testing.expectError(error.Underflow, powi(i8, -66, 6));
try testing.expectError(error.Underflow, powi(i16, -13, 13));
try testing.expectError(error.Underflow, powi(i32, -32, 21));
try testing.expectError(error.Underflow, powi(i64, -24, 61));
try testing.expectError(error.Underflow, powi(i17, -15, 15));
try testing.expectError(error.Underflow, powi(i42, -6, 40));
try testing.expect((try powi(i8, -5, 3)) == -125);
try testing.expect((try powi(i16, -16, 3)) == -4096);
try testing.expect((try powi(i32, -91, 3)) == -753571);
try testing.expect((try powi(i64, -36, 6)) == 2176782336);
try testing.expect((try powi(i17, -2, 15)) == -32768);
try testing.expect((try powi(i42, -5, 7)) == -78125);
try testing.expect((try powi(u8, 6, 2)) == 36);
try testing.expect((try powi(u16, 5, 4)) == 625);
try testing.expect((try powi(u32, 12, 6)) == 2985984);
try testing.expect((try powi(u64, 34, 2)) == 1156);
try testing.expect((try powi(u17, 16, 3)) == 4096);
try testing.expect((try powi(u42, 34, 6)) == 1544804416);
try testing.expectError(error.Overflow, powi(i8, 120, 7));
try testing.expectError(error.Overflow, powi(i16, 73, 15));
try testing.expectError(error.Overflow, powi(i32, 23, 31));
try testing.expectError(error.Overflow, powi(i64, 68, 61));
try testing.expectError(error.Overflow, powi(i17, 15, 15));
try testing.expectError(error.Overflow, powi(i42, 121312, 41));
try testing.expectError(error.Overflow, powi(u8, 123, 7));
try testing.expectError(error.Overflow, powi(u16, 2313, 15));
try testing.expectError(error.Overflow, powi(u32, 8968, 31));
try testing.expectError(error.Overflow, powi(u64, 2342, 63));
try testing.expectError(error.Overflow, powi(u17, 2723, 16));
try testing.expectError(error.Overflow, powi(u42, 8234, 41));
}
test "math.powi.special" {
try testing.expectError(error.Underflow, powi(i8, -2, 8));
try testing.expectError(error.Underflow, powi(i16, -2, 16));
try testing.expectError(error.Underflow, powi(i32, -2, 32));
try testing.expectError(error.Underflow, powi(i64, -2, 64));
try testing.expectError(error.Underflow, powi(i17, -2, 17));
try testing.expectError(error.Underflow, powi(i42, -2, 42));
try testing.expect((try powi(i8, -1, 3)) == -1);
try testing.expect((try powi(i16, -1, 2)) == 1);
try testing.expect((try powi(i32, -1, 16)) == 1);
try testing.expect((try powi(i64, -1, 6)) == 1);
try testing.expect((try powi(i17, -1, 15)) == -1);
try testing.expect((try powi(i42, -1, 7)) == -1);
try testing.expect((try powi(u8, 1, 2)) == 1);
try testing.expect((try powi(u16, 1, 4)) == 1);
try testing.expect((try powi(u32, 1, 6)) == 1);
try testing.expect((try powi(u64, 1, 2)) == 1);
try testing.expect((try powi(u17, 1, 3)) == 1);
try testing.expect((try powi(u42, 1, 6)) == 1);
try testing.expectError(error.Overflow, powi(i8, 2, 7));
try testing.expectError(error.Overflow, powi(i16, 2, 15));
try testing.expectError(error.Overflow, powi(i32, 2, 31));
try testing.expectError(error.Overflow, powi(i64, 2, 63));
try testing.expectError(error.Overflow, powi(i17, 2, 16));
try testing.expectError(error.Overflow, powi(i42, 2, 41));
try testing.expectError(error.Overflow, powi(u8, 2, 8));
try testing.expectError(error.Overflow, powi(u16, 2, 16));
try testing.expectError(error.Overflow, powi(u32, 2, 32));
try testing.expectError(error.Overflow, powi(u64, 2, 64));
try testing.expectError(error.Overflow, powi(u17, 2, 17));
try testing.expectError(error.Overflow, powi(u42, 2, 42));
try testing.expect((try powi(u8, 6, 0)) == 1);
try testing.expect((try powi(u16, 5, 0)) == 1);
try testing.expect((try powi(u32, 12, 0)) == 1);
try testing.expect((try powi(u64, 34, 0)) == 1);
try testing.expect((try powi(u17, 16, 0)) == 1);
try testing.expect((try powi(u42, 34, 0)) == 1);
}
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